Use synthetic division to solve (x4 – 1) ÷ (x – 1). what is the quotient?

The correct answer is:

x³+x²+x+1.

Explanation:

First we write the polynomial out with all of the other powers of x, using 0 as their coefficients:

(1x⁴+0x³+0x²+0x-1)÷(x-1)

To perform synthetic division, we write the coefficients of the dividend in a row:

1 0 0 0 1

We take the 1 from x-1 and use it in the box. We then drop the first 1 from the row of coefficients down.

We multiply our 1 in the box by the 1 at the bottom; this is 1 and goes under the first 0 to the right of the 1 in the coefficients row. We now add this 0+1; this is 1 and goes at the bottom beside the other 1.

Multiply this by 1; this is 1 and goes under the second 0 from the left in the row of coefficients. Add this to the 0; this is 1 and goes at the bottom, to the right of the other two 1's.

Multiply this by 1; this is 1 and goes under the third and last 0 in the row of coefficients. Add this to the 0; this is 1 and goes at the bottom, to the right of the other three 1's.

Multiply this by 1; this is 1 and goes under the -1 in the row of coefficients. Add this to the -1; this is 0 and goes at the bottom, to the right of the four 1's. This 0 means there is no remainder and the quotient was evenly divided. It gives us

1 1 1 1 0

This means we have 1x³+1x²+1x+1 with no remainder.

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490

1.0

step-by-step explanation: